Minimum of a tan^2 + b cot^2 or a sec^2 + b cosec^2 by AM-GM

This type of question, asked 3 times: CDS 1 2017, CDS 1 2020, CDS 2 2022. All 3 questions below, oldest first.

Try each one first, then open its answer.

Question 1
CDS 1 2017
60 $9 \tan^2 \theta + 4 \cot^2 \theta$
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Question 2
CDS 1 2020
52 $(25\,\operatorname{cosec}^2 x + \sec^2 x)$
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Question 3
CDS 2 2022
59 $3600\sec^2\theta + 121\operatorname{cosec}^2\theta$
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